Speaker John A. Boehner, R-Ohio and Minority Leader Nancy Pelosi, D-Calif., don't find common ground on a lot of issues, but both lawmakers staked out similar positions Thursday on Eric Shinseki, rebuffing calls for the embattled Veterans Affairs secretary's resignation.

Boehner said it's premature to talk of firing Shinseki, who is under pressure from dozens of lawmakers to step down in the wake of new revelations of poor care at VA hospitals. "The question I ask myself is, is him resigning going to get us to the bottom of the problem? Is it going to help us find out what’s really going on. And the answer I keep getting is 'no,'" the speaker told reporters Thursday at his weekly briefing.

Pelosi echoed those comments at her news conference.

“They kept the information form the secretary and the Congress. So let’s reward them by removing the secretary?” Pelosi asked.

About two hours later, House Majority Leader Eric Cantor, R-Va., criticized the Obama administration's handling of the crisis but stopped short of calling for Shinseki's resignation.

"Veterans deserve more than the resignation of one man," Cantor said in another briefing with reporters. "Accountability for this starts at the very top."

The comments from the top party leaders in the House came one day after the VA inspector general's release of a damning 35-page report that found 1,700 veterans were secretly waiting for a preliminary appointment at the Phoenix medical facility, and followed a high-profile VA hearing Wednesday night that further called into question the VA's response to the scandal.